#10813Traditional BINGO

The number of unique BINGO cards is very large and can be calculated with this equation:

// the B, I, G, and O columns * the N column

While perhaps interesting to a statistician, the number of possible BINGO cards has nothing to do with player's chances of winning.

You will note that there are 75 possible BINGO numbers:

B1, B2, B3, ... B15,
I16, I17, I18, ... I30,
N31, N32, ..., N45,
G46, G47, ..., G60,
O61, ..., O74, O75.

Each of these numbers is represented by a ball in a large rotating bin. Each ball is painted with its unique BINGO number. An announcer spins the bin, reaches in a selects a ball, and a announces it to the room. The players check all of their cards to see if that number appears on their card. If it is, they mark it. A player may mark the centre FREE SPACE at any time.

When a player has a BINGO (5 marks in a row, column, or diagonal), he or she calls out BINGO. The game pauses while the card is verified. If indeed a winner, the game stops and a new game begins. If the card wasn't a winner, the game proceeds where it left off. Each BINGO game proceeds until someone wins (there's always a winner).

Input

The first line of input contains n, the number of BINGO games that you will analyze. n game descriptions follow. Each game description specifies a card to be played followed by a sequence of BINGO numbers. You are to determine, when the holder of the card will win the game, assuming the player has just this one card and there are no other players.

Each card description consists of five lines, giving the numbers on the card row by row. All but the 3rd row contain 5 numbers; the 3rd contains 4 because of the free space. One or more lines follow that represent some ordering of all 75 bingo numbers. All bingo numbers are simply integers between 1 and 75 — the one-letter prefix is redundant.

Output

For each game, ouput the line 'BINGO after n numbers announced' as appropriate.

Chances of Winning

Every BINGO game has a winning card, so a player's chances of winning depend on the number of cards in the game and how many cards s/he is playing. For example, if a player has 12 cards in a game with 1200 cards, the chances of winning for that player is 1 in 100.